The monthly demand function for a product sold by a monopoly is

Question

p = 3750 − 1/3x^2 dollars, and the average cost is C = 1000 + 70x + 3x^2
dollars. Production is limited to 1000 units and x is in hundreds of units.
(a) Find the quantity that will give maximum profit.
(b) Find the maximum profit. (Round your answer to the nearest cent.)

Answer 1

profit = revenue - cost
revenue = price * quantity
cost = avg cost * quantity

No indication is given regarding price per unit.

Answer 2

I've done p= x(3750 − 1/3x^2) and C = x(1000 + 70x + 3x^2)
Profit= 3750x-1/3x^3-1000x-70x^2-3x^3= 2750x-70x^2-4/3x^3

P'(x)= 2750-140x-12x^2
Then I did the Quadratic Formula and and got 22 but it's wrong

Answer 3

There seems to be something wrong here.
It appears that x is the selling price, making

x(3750 − 1/3x^2) the revenue

But how can the average cost C be dependent on the selling price?

Are you somehow mixing up x, making it the price in one place and the quantity in another?